Question: Simplify the following expression: $p = \dfrac{5n^2 + 35n - 40}{n - 1} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ p =\dfrac{5(n^2 + 7n - 8)}{n - 1} $ Then we factor the remaining polynomial: $n^2 + {7}n {-8} $ ${-1} + {8} = {7}$ ${-1} \times {8} = {-8}$ $ (n {-1}) (n + {8}) $ This gives us a factored expression: $\dfrac{5(n {-1}) (n + {8})}{n - 1}$ We can divide the numerator and denominator by $(n + 1)$ on condition that $n \neq 1$ Therefore $p = 5(n + 8); n \neq 1$